Paul McCartney is a neighbor to this Amagansett house

Sir Paul McCartney will be your neighbor if you buy this Amagansett house. The home also comes a wine cellar and a heated pool surrounded by a large outdoor deck. It is on the market in July 2015, for $1.725 million. Photo Credit: Town & Country Real Estate / Chris Foster

Listing agent Richard Swift of Town & Country Real Estate says that since the wooded property is so private, McCartney "can't come out of his window and say, 'Can I borrow a cup of sugar?' "

Aside from the possibility of bumping into Sir Paul -- who bought into the neighborhood in 1998, according to published reports -- Swift says the home is one of the few renovated properties in Amagansett for less than $2 million.

"It's two minutes to the ocean, it's two minutes to Main Street," Swift says.